Abstract
In everyday life, optical devices that reverse the direction of all (or a significant part of) incident beams of light are called retroreflectors. They are widely used in technology, for example, in road safety. Some artificial satellites in Earth’s orbit also carry retroreflectors. We are mostly interested in perfect retroreflectors that reverse the direction of any incident beam of light to the exact opposite direction. An example of perfect retroreflector based on light refraction is the Eaton lens, a transparent ball with varying radially symmetric refractive index going to infinity at the center [19,71]. Each incident light ray, after making a curve in the lens around the center, leaves in the direction exactly opposite to the direction of incidence. On the other hand, no perfect retroreflector based solely on light reflection (rather than refraction) is known.
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Notes
- 1.
Recall that the angle φ is measured counterclockwise from the vertical vector (0, 1) to the velocity of the incident particle, so one has φ < 0 in Fig. 9.10.
- 2.
Notice that m depends on δ and \(\tilde{{z}}_{0}\); thus, strictly speaking, one should write \(m = {m}_{\delta }(\tilde{{z}}_{0})\). Then the equality holds \({m}_{\delta }(\tilde{{z}}_{0}) = {m}_{\gamma }(\tilde{{x}}_{0},\lambda )\), where sinγ = tanhδ and \(\tilde{{x}}_{0} = {e}^{-\delta \tilde{{z}}_{0}}\); recall that the parameter λ is fixed.
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Plakhov, A. (2012). Retroreflectors. In: Exterior Billiards. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4481-7_9
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